Answer :
Alright, let's solve the problem step-by-step.
Given:
- An isosceles triangle with a perimeter of 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
We need to find the equation that can be used to determine the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] represents the lengths of the two equal sides of the triangle.
### Step-by-Step Solution
1. Understanding the Perimeter of an Isosceles Triangle:
The perimeter [tex]\( P \)[/tex] of a triangle is the sum of all its sides. For an isosceles triangle, if two sides are equal and one side is different, the perimeter is given by:
[tex]\[
P = x + x + y
\][/tex]
Here, the two equal sides are [tex]\( x \)[/tex] each, and the third side is [tex]\( y \)[/tex].
2. Substitute the Given Values:
- Perimeter [tex]\( P = 7.5 \)[/tex] meters.
- Shortest side [tex]\( y = 2.1 \)[/tex] meters.
The equation now looks like:
[tex]\[
7.5 = x + x + 2.1
\][/tex]
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation. Start by subtracting 2.1 from both sides:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
[tex]\[
5.4 = 2x
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
So, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]
Given:
- An isosceles triangle with a perimeter of 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
We need to find the equation that can be used to determine the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] represents the lengths of the two equal sides of the triangle.
### Step-by-Step Solution
1. Understanding the Perimeter of an Isosceles Triangle:
The perimeter [tex]\( P \)[/tex] of a triangle is the sum of all its sides. For an isosceles triangle, if two sides are equal and one side is different, the perimeter is given by:
[tex]\[
P = x + x + y
\][/tex]
Here, the two equal sides are [tex]\( x \)[/tex] each, and the third side is [tex]\( y \)[/tex].
2. Substitute the Given Values:
- Perimeter [tex]\( P = 7.5 \)[/tex] meters.
- Shortest side [tex]\( y = 2.1 \)[/tex] meters.
The equation now looks like:
[tex]\[
7.5 = x + x + 2.1
\][/tex]
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation. Start by subtracting 2.1 from both sides:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
[tex]\[
5.4 = 2x
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
So, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]
